The couple, who were introduced by Ed Sheeran, recently moved in together in Malibu and although their relationship is ''very serious'' the former 'Friends' star, who was previously married to David Arquette, isn't thinking about re-marrying just yet.

A source said: ''She is just being in love.''

The Snow Patrol rocker, 37, is set to accompany the 49-year-old actress - who has nine-year-old daughter Coco with her ex-husband - to the Tribeca Film Festival in New York City on April 24, where her directorial debut, 'Just Before I Go,' will be screened for the first time.

The insider told Us Weekly magazine: ''His support means so much to her.''

While the pair have no plans to marry, their mutual friend Ed recently said he won't be surprised if they tie the knot one day.

Asked if he thinks they will marry, the 'A Team' hitmaker said: ''I wouldn't be surprised, but it's still early days.

''They certainly enjoy each other's company and feel very comfortable with each other.''